A gravity model turns a catchment into a sales forecast in four steps, and the tenants' reported sales tell you which distance exponent to believe.
The Huff model gives each centre a share of every residential zone's spending in proportion to its size divided by travel time squared, then adds the zones up. On an illustrative catchment of 240,000 people spending 432 million a year in store, a 30,000 m² centre competing with a 60,000 m² mall and a town centre captures 188.5 million, 43.6 per cent of the pool, or 6,282 per m². The answer is only as good as the distance exponent, so calibrate it against the sales the tenants actually report.
Worked in full in Retail Real Estate by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
David Huff's 1963 model treats shopping as a probability. A household in zone i chooses centre j with a probability that rises with the centre's attractiveness, usually its floorspace, and falls with the time it takes to get there.
Pij = (Sjα / Tijλ) / Σk (Skα / Tikλ)
Salesj = Σi Pij × populationi × spend per head
Excel, one zone per row: =(Size_j/Time_ij^Lambda)/SUMPRODUCT(Sizes/Times_i^Lambda)
Here α = 1.0 and λ = 2.0, the textbook starting point. Attractiveness can include more than floorspace, an anchor, parking, a cinema, but every added term needs its own exponent and its own evidence.
All figures are illustrative. Spend per head is 2,250 a year in the categories a centre sells, less 20 per cent that goes online, so 1,800 is spent in store.
| Zone | Population | In-store spend | Subject, 30,000 m² | Mall, 60,000 m² | Town, 15,000 m² |
|---|---|---|---|---|---|
| Zone 1 | 50,000 | 90,000,000 | 10 | 25 | 15 |
| Zone 2 | 80,000 | 144,000,000 | 15 | 15 | 25 |
| Zone 3 | 40,000 | 72,000,000 | 20 | 30 | 10 |
| Zone 4 | 70,000 | 126,000,000 | 12 | 20 | 20 |
| Catchment | 240,000 | 432,000,000 |
Step 1, utility of each centre from each zone. Size over time squared. From Zone 1: subject 30,000 / 10² = 300.00; mall 60,000 / 25² = 96.00; town 15,000 / 15² = 66.67.
Step 2, probabilities. Divide each by the zone total, 462.67: subject 64.8 per cent, mall 20.7, town 14.4.
Step 3, sales from the zone. 64.8% × 90,000,000 = 58.4 million to the subject.
Step 4, repeat and add.
| Zone | Utilities: subject, mall, town | Subject share | Subject sales, m |
|---|---|---|---|
| Zone 1 | 300.00 / 96.00 / 66.67 | 64.8% | 58.4 |
| Zone 2 | 133.33 / 266.67 / 24.00 | 31.4% | 45.3 |
| Zone 3 | 75.00 / 66.67 / 150.00 | 25.7% | 18.5 |
| Zone 4 | 208.33 / 150.00 / 37.50 | 52.6% | 66.3 |
| Total | 43.6% | 188.5 |
The same arithmetic gives the mall 173.4 million and the town centre 70.1 million, and the three add back to the 432 million pool. Per m², the subject trades at 6,282, the town centre at 4,672 and the mall at 2,891: the mall is twice the size but sits far from most of the population.
| λ | Sales, m | Share | Per m² | Against base |
|---|---|---|---|---|
| 1.0 | 157.8 | 36.5% | 5,261 | -16.3% |
| 1.5 | 174.0 | 40.3% | 5,800 | -7.7% |
| 2.0 | 188.5 | 43.6% | 6,282 | 0.0% |
| 2.5 | 201.0 | 46.5% | 6,699 | 6.6% |
| 3.0 | 211.5 | 49.0% | 7,052 | 12.2% |
A centre that is close to its customers gains as distance matters more. The exponent is not a universal constant: it is lower for a destination mall people will drive to, higher for convenience shopping. This is where retail has an advantage no other asset class has. The tenants report their sales, so the model can be calibrated: if the subject's tenants report about 174 million, λ is nearer 1.5 than 2.0, and the scenarios below should be run at that value.
Sales density feeds rent directly. At a 10 per cent occupancy cost ceiling and 120 per m² of service charge and rates, 6,282 supports 508 per m² of rent; a 12.5 per cent fall in sales cuts that capacity by more than 12.5 per cent, because the costs do not fall with it.
Turning sales into the rent each unit can sustain is the subject of the free workbook for this case; the per-unit measure is worked in how to calculate sales per square foot in retail.
Start at 2.0 and calibrate it to observed sales. Destination centres usually fit a lower value, convenience shopping a higher one. In the illustrative catchment the subject's sales move from 157.8 million at 1.0 to 211.5 million at 3.0, so if tenants report about 174 million the exponent is nearer 1.5 and every scenario should be run there.
Fewer than the existing space, because the extension only raises the centre's attractiveness against the same competitors. In the worked Huff model a 6,000 m² extension to a 30,000 m² centre adds 17.8 million of sales, 2,962 per m², while the existing space averages 6,282. Value the extension on the marginal figure, not the average.
Yes, through spend per head rather than through the shares. If the online share of the categories rises from 20 to 30 per cent, in-store spend per head falls from 1,800 to 1,575 and the illustrative centre's sales fall 12.5 per cent, from 188.5 to 164.9 million, with no change in competition.
This article is one calculation from Retail Real Estate. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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